The 51st known Mersenne prime was discovered on December 7, 2018. It is: Source: https://www.mersenne.org.
New correction sheet for the actual book-version
The new correction sheet (as of 27.11.2018) is available as a PDF in the download section. There are a few minor corrections concerning Perrin sequences in chapters 4.10.1.4 and 20.3.
New: Supplement for the book (about virtual OCRONs, Matula-Goebel numbers, Jacobi-Addition)
In the download area a supplement for the chapter 20.8 (vrtual OCRONs) is available for download. Interesting new, unexpected connections arise between the theory of graphs (Matula-Goebel numbers) and theory of prime numbers! ->get supplement The ‘hierarchies’ of arithmetic are also reflected by the principle of virtual OCRONs ..
50th known Mersenne prime number has been found
On December 26, 2017, the 50th known Mersenne prime was found: 2 raised to a power of 77232917-1. This number contains 23249425 digits if written in the decimal system. It is the largest currently known prime number. The discoverer is Jonathan Pace, an electrical engineer from Germantown Tennesse, USA. More info: http://www.mersenne.org
Gadgets with the Ulam spiral: Computation and visualization of prime numbers and more…
This interactive CDF computes the Ulam Spiral for a given start value 0,1,2,.. which can also be negative. Interesting structures of the Ulam spiral can be seen on the 4 horizontal/vertical and 4 diagonal lines in the four quadrants. Those 8 lines belong to an startpoint, which can also be offset to the center of…
animation of the zeta function showing the zeros
animation of the zeta function along the critical line by using the product representation (complex doman)